People in the wizarding world are seen wearing pocket watches. The reason for which maybe that the objects used by wizards and witches (as quills, oil lamps, candles, ect.) are not as modern as objects used by Muggles. Pocket watches are one of which, which have not been as widely used as the pre-WWI era. Also, in the wizarding world, one is given a watch when they turn of age. Dumbledore, for instance, would have turned 17 when pocket watches were still in style. There is a Transfigurationspell capable of turning a human into a pocket watch. Known wizards and witches to own pocket watches include:

Behind the scenes

It is not specified what type of watch Harry Potter was given when he turned of age. However, due to the fact that it was dented on the back, it was probally indeed a pocket watch, as the back of a wristwatch is against the wrist when in use. In this case, Ron Weasley also has a pocket watch, as Harry's was "like what Ron got."